Differential Test Functioning via Robust Scaling
Peter F. Halpin
[stat.ME]
In the item response theory (IRT) literature, differential test functioning (DTF) has been conceptualized in terms of how the test response function differs over groups of respondents. This paper presents an alternative approach to DTF that focusses on how the distribution of the latent trait differs over groups, which is referred to as impact. We propose to compare two estimates of impact, one that naively aggregates over all test items and one that down-weights items that exhibit differential item functioning (DIF). Taking this approach, we make the following three contributions to the literature on DTF. First it is shown that the difference between the two estimates provides a convenient effect size for quantifying the extent to which DIF affects conclusions about impact (as opposed to test scores). Second, we provide a relatively general purpose Wald test of the difference between two estimates of impact. Third, we extend the recent literature on robust scaling to propose a procedure for down-weighting items that is shown to produce consistent estimates of impact whenever fewer than 1/2 of items exhibit DIF. Using simulations and an empirical example from physics education, we show how the proposed effect size and test statistic perform using the proposed robust estimator of impact, as well as estimators that arise from conventional item-by-item tests of DIF.